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 A308267 Numbers k such that k divides A048678(k). 0
 1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 83, 112, 124, 127, 128, 166, 224, 248, 254, 256, 332, 397, 448, 496, 508, 511, 512, 664, 794, 891, 896, 992, 1016, 1022, 1024, 1163, 1328, 1588, 1782, 1792, 1984, 2032, 2044, 2047, 2048, 2326, 2656, 3176, 3441, 3564, 3584, 3968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Apparently includes all powers of 2. All numbers 2^(2k+1)-1 are in this sequence, and if n is in this sequence then so is 2n. - Charlie Neder, May 17 2019 LINKS Table of n, a(n) for n=1..55. EXAMPLE The first few terms of A048678 are 1,2,5,4,9,10,21,8. 2 is a multiple of 2, 5 isn't a multiple of 3, 4 is a multiple of 4, 9 isn't a multiple of 5, 10 isn't a multiple of 6, 21 is a multiple of 7, etc. MATHEMATICA Select[Range[4000], Divisible[FromDigits[Flatten[IntegerDigits[#, 2] /. {1 -> {0, 1}}], 2], #] &] (* Amiram Eldar, Jul 08 2019 after Robert G. Wilson v at A048678 *) PROG (Haskell) bintodec :: [Integer] -> Integerbintodec = sum . zipWith (*) (iterate (*2) 1) . reverse decomp :: (Integer, [Integer]) -> (Integer, [Integer])decomp (x, ys) = if even x then (x `div` 2, 0:ys) else (x - 1, 1:ys) zeck :: Integer -> Integerzeck n = bintodec (1 : snd (last . takeWhile (\(x, _) -> x > 0) \$ iterate decomp (n, []))) output :: [Integer]output = filter (\x -> 0 == zeck x `mod` x) [1..100] main :: IO ()main = print output CROSSREFS Cf. A048678, A083420 (subsequence). Sequence in context: A324588 A201364 A225318 * A177805 A003591 A029746 Adjacent sequences: A308264 A308265 A308266 * A308268 A308269 A308270 KEYWORD nonn,base AUTHOR Dan Dart, May 17 2019 STATUS approved

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)